Problem: Solve for $x$ and $y$ using substitution. ${6x-4y = 10}$ ${y = 3x+2}$
Answer: Since $y$ has already been solved for, substitute $3x+2$ for $y$ in the first equation. ${6x - 4}{(3x+2)}{= 10}$ Simplify and solve for $x$ $6x-12x - 8 = 10$ $-6x-8 = 10$ $-6x-8{+8} = 10{+8}$ $-6x = 18$ $\dfrac{-6x}{{-6}} = \dfrac{18}{{-6}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = 3x+2}\thinspace$ to find $y$ ${y = 3}{(-3)}{ + 2}$ $y = -9 + 2$ $y = -7$ You can also plug ${x = -3}$ into $\thinspace {6x-4y = 10}\thinspace$ and get the same answer for $y$ : ${6}{(-3)}{ - 4y = 10}$ ${y = -7}$